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Geometry › Symmetry
Symmetry
A shape is symmetric if it looks the same after a fold, a turn, or a slide.
Symmetry folder
Pick a fold line, then press Fold. Or draw your own shape and check it.
Fold line
♥ — vertical only.
H — vertical and horizontal.
F — none.
When the dashed mirror copy lines up with the solid shape, that fold line is a line of symmetry.
Three kinds of symmetry
- Reflection — fold the shape along a line. The two halves match.
- Rotational — turn the shape and it looks identical at certain angles.
- Translational — slide the shape along a direction (used in tiling and patterns).
Lines of symmetry
A square has 4 lines of symmetry (two diagonals + horizontal + vertical). A regular pentagon has 5. A circle has infinitely many — you can fold it along any line through its center.
Order of rotation
A shape has rotational symmetry of order n if it looks the same n times when turning a full 360°. A square has order 4 (90°, 180°, 270°, 360°). A regular hexagon has order 6.
In the wild
- Snowflakes — six-fold rotational symmetry.
- Butterflies — line symmetry (vertical).
- Wallpaper patterns — translational symmetry.
- Letters: A, M, T are vertical-line symmetric; H, I, O have both vertical and horizontal; S, N, Z have rotational symmetry of order 2.